Calendar

Mar
1
Thu
Colloquium: Andrew Sale (Cornell U. )
Mar 1 @ 3:00 pm – 4:00 pm

Speaker: Andrew Sale (Cornell U.)

Title: On the outer automorphism groups of right-angled Artin and Coxeter groups

Abstract: In geometric group theory, a fundamental, and broad, question to answer is that of understanding the world of finitely presented groups. Two of the simplest examples are free groups Fn and free abelian groups Z^n. With Fn and Z^n being their extreme examples, right-angled Artin groups (RAAGs) give us some idea of what happens “between” these groups. RAAGs are an important class of groups which appear in diverse situations, perhaps most significantly in Agol’s proof of the virtual Haken conjecture.

In studying their outer automorphism groups, we are looking at a class of groups that again interpolates between two classically important families of groups: Out(Fn), the outer automorphism group of Fn, and GL(n,Z). While there are numerous similarities between these families, they also differ in some important contexts. One such context concerns the nature of quotients that they have, and I will describe a couple of properties that make rigorous the notion of “having many quotients”. I will explain what happens for outer automorphism groups of RAAGs, and also the closely related family of right-angled Coxeter groups, and the consequences this has for Kazhdan’s Property (T).

Mar
5
Mon
Colloquium: Sam Nariman
Mar 5 @ 3:30 pm – 4:30 pm

Speaker: Sam Nariman (Northwestern U.)

Title: On the homology of diffeomorphism groups made discrete.

Abstract: Let $G$ be a finite dimensional Lie group and $G^{delta}$ be the same group with the discrete topology. The classifying space $BG$ classifies principal $G$-bundles and the classifying space $BG^{delta}$ classifies flat principal $G$-bundles (i.e. those bundles that admit a connection whose curvature vanishes). The natural homomorphism from $G^{delta}$ to $G$ induces a continuous map from $BG^{delta}$ to $BG$. Milnor conjectured that this map induces an equivalence after the profinite completion. In this talk, we discuss the same map for infinite dimensional Lie groups, in particular for diffeomorphism groups and symplectomorphisms. In these cases, we use techniques from homotopy theory to show that the map from $BG^{delta}$ to $BG$ induces a split surjection on cohomology with finite coefficients in the stable range. If time permits, I will discuss applications of these results in foliation theory, in particular, characteristic classes of​ flat surface bundles.

Mar
16
Fri
Talk Story with Thomas Hangelbroek
Mar 16 @ 3:30 pm – 4:30 pm
Mar
23
Fri
Colloquium: Christopher Marks (Cal. State Chico)
Mar 23 @ 3:30 pm – 4:30 pm
Apr
12
Thu
Undergraduate Seminar: Alex Schulte (Iowa State U.) @ Keller 402
Apr 12 @ 3:00 pm – 4:00 pm
Apr
17
Tue
Analysis Qualifying Exam
Apr 17 @ 9:00 am – 1:00 pm
Apr
24
Tue
Algebra Qualifying Exam
Apr 24 @ 9:00 am – 1:00 pm
May
22
Tue
Algebras and Lattices in Hawaii
May 22 – May 24 all-day